Now, I never figured out the naming scheme for AF and having taken a 4 year break, that has only gotten more confusing. AF1, AF2, AF3, AF3+2... I feel like I am in college algebra.
"AF1", "AF2" and "AF3" used to refer to the Artifact Armor quest line. So AFX used to refer to either the quest itself or the piece of Artifact gear you received from it.
These days, AF1 (or just AF) is more likely to refer to the Artifact armor line that every job gets in the 50s (along with the Artifact weapon they get in the early 40s). AF2 likely refers to Relic gear, which is obtained in Dynamis and can be equipped in the 70s. AF3 is the Empyrean line, which can be obtained through Abyssea and can be equipped in the 80s.
The original Artifact armor sets can be upgraded to +1 versions through Limbus. That would be AF1+1 (or maybe just AF+1). Relic gear can also be upgraded to +1, and now +2 versions (AF2+1/2). Empyrean can be upgraded to +1 and +2 versions (AF3+1/2).
I prefer to type a few extra letters for nomenclature that's easier to identify when reading, such as Relic +1/+2 or Empy +1/+2.
Lyonheart of Lakshmi
lvl 99 NIN WAR BST THF BLM SCH WHM
1/467 on signed HQ Weskit!!!